The electronic energy band structure and the optical properties of gamma-Ag3SI are calculated by using density functional theory under the local density approximation (LDA). The calculated electronic band structure shows that gamma-Ag3SI has an indirect gap with a value of 0.46 eV at the M -> Gamma points in the Brillouin zone. A structural optimization has been performed by using the LDA. The optical spectra of the gamma-Ag3SI in the photon range up to 30 eV are calculated by using a first-principles method under the scissor approximation. The real and the imaginary parts of the dielectric function as functions of the photon energy and, thus, the optical constants, such as the energy-loss function, the refractive index, and the effective number of electrons, are investigated. The calculated structural optimization of gamma-Ag3SI is compared with the experimental results and is found to be in good agreement with the experimental data.